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In [[category theory]], a '''functor''' is a type of function between categories. Functors can be thought of as [[morphism]]s in the category of small categories.

In [[category theory]], a '''functor''' is a type of function between categories. Functors can be thought of as [[morphism]]s in the category of categories.

Functors were first proposed in [[algebraic topology]], where algebraic objects such as the [[fundamental group]] are associated to [[topological space]]s, and algebraic [[homomorphism]]s are associated to continuous functions.  Recently, functors are used to relate various categories.

Functors were first proposed in [[algebraic topology]], where algebraic objects such as the [[fundamental group]] are associated to [[topological space]]s, and algebraic [[homomorphism]]s are associated to continuous functions.  Recently, functors are used to relate various categories.